Question: Simplify the following expression: $\dfrac{54q^3}{72q^4}$ You can assume $q \neq 0$.
Answer: $ \dfrac{54q^3}{72q^4} = \dfrac{54}{72} \cdot \dfrac{q^3}{q^4} $ To simplify $\frac{54}{72}$ , find the greatest common factor (GCD) of $54$ and $72$ $54 = 2 \cdot 3 \cdot 3 \cdot 3$ $72 = 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3$ $ \mbox{GCD}(54, 72) = 2 \cdot 3 \cdot 3 = 18 $ $ \dfrac{54}{72} \cdot \dfrac{q^3}{q^4} = \dfrac{18 \cdot 3}{18 \cdot 4} \cdot \dfrac{q^3}{q^4} $ $\phantom{ \dfrac{54}{72} \cdot \dfrac{3}{4}} = \dfrac{3}{4} \cdot \dfrac{q^3}{q^4} $ $ \dfrac{q^3}{q^4} = \dfrac{q \cdot q \cdot q}{q \cdot q \cdot q \cdot q} = \dfrac{1}{q} $ $ \dfrac{3}{4} \cdot \dfrac{1}{q} = \dfrac{3}{4q} $